“He is very bright. He is a very good minister. I am sure he will be a major figure in the party for a long time to come and a major contender at some time in the future.

“But should he take this step to satisfy someone else’s prejudices? He would be daft.”

Mr Miliband, Secretary for Environment, Food and Rural Affairs, has been mooted as a candidate who would appeal to supporters of Tony Blair.

Mrs Beckett said Labour has plenty of potential leaders but added that the Chancellor is “head and shoulders” ahead of any other potential candidate to succeed Blair in the summer, saying a contest would be “artificial” and a waste of Labour’s time and money.